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Abstract

We develop and validate a Modified Beer-Lambert law for blood flow based on diffuse correlation spectroscopy (DCS) measurements. The new formulation enables blood flow monitoring from temporal intensity autocorrelation function data taken at single or multiple delay-times. Consequentially, the speed of the optical blood flow measurement can be substantially increased. The scheme facilitates blood flow monitoring of highly scattering tissues in geometries wherein light propagation is diffusive or non-diffusive, and it is particularly well-suited for utilization with pressure measurement paradigms that employ differential flow signals to reduce contributions of superficial tissues.

M. Cope, “The development of a near infrared spectroscopy system and its application for non invasive monitoring of cerebral blood and tissue oxygenation in the newborn infants,” Ph.D. thesis, University of London (1991).

M. Cope, “The development of a near infrared spectroscopy system and its application for non invasive monitoring of cerebral blood and tissue oxygenation in the newborn infants,” Ph.D. thesis, University of London (1991).

Other (6)

M. Cope, “The development of a near infrared spectroscopy system and its application for non invasive monitoring of cerebral blood and tissue oxygenation in the newborn infants,” Ph.D. thesis, University of London (1991).

(A) The semi-infinite multiplicative weighting factors (see Eq. (4)) for tissue scattering (ds), for tissue absorption (da), and for tissue blood flow (dF, right vertical-axis). They are plotted as a function of the correlation time, τ, for source-detector separation, ρ = 3 cm, and optical wavelength, λ = 785 nm, given a typical set of cerebral tissue properties, i.e.,
μa0=0.1cm−1,
μs′0=8cm−1, F0 = 10−8 cm2/s, n = 1.4, nout = 1. (B) The semi-infinite DCS Modified Beer-Lambert components dF (τ, ρ)ΔF, ds(τ, ρ)Δμ′s, and |da(τ, ρ)Δμa|, plotted as a function of τ for a 10% increase in blood flow, tissue scattering, and tissue absorption, respectively. On the right vertical-axis is the intensity autocorrelation function,
g20(τ), for β = 0.5. Given the same fractional change in tissue properties, the DCS signal is most sensitive to scattering changes, followed by flow changes, and finally absorption changes. In many applications, however, the scattering changes associated with hemodynamic perturbations are negligible, e.g., such as an increase in blood flow and blood volume; in these situations the scattering component can be neglected (see text).

(A) The two-layer multiplicative weighting factors (see Eq. (9)) for dF,c and dF,ec (right vertical-axis); and for da,c, da,ec, ds,c, and ds,ec. They are plotted as a function of the correlation time, τ, for source-detector separation, ρ = 3 cm, and optical wavelength, λ = 785 nm, given a set of typical extra-cerebral and cerebral tissue properties [51], i.e.,
μa,c0=0.16,
μa,ec0=0.12,
μs,c′0=6,
μs,ec′0=10cm−1;
Fc0=10−8,
Fec0=10−9cm2/s; ℓ = 1 cm, n = 1.4, and nout = 1. (B) The two-layer DCS Modified Beer-Lambert components dF,cΔFc, dF,ecΔFec, |da,cΔμa,c|, and |da,ecΔμa,ec|, plotted as a function of τ for a 10% increase in each parameter. On the right vertical-axis is the intensity autocorrelation function,
g20(τ), for β = 0.5. Notice that at shorter delay-times for ρ = 3 cm, the change in DCS optical density is equally sensitive to changes in cerebral blood flow, extra-cerebral blood flow, and cerebral absorption. The change in DCS optical density (ODDCS) is less sensitive, however, to changes in extra-cerebral absorption. (C) The ratio of the cerebral (c) and extra-cerebral (ec) flow components in the DCS optical density perturbation, ΔODDCS(τ) (Eq. (9)), for 4 separations, ρ = 0.5, 1, 2, and 3 cm. These data are plotted as a function of τ assuming a 10% increase in cerebral and extra-cerebral blood flow. For the shorter separations of 0.5 and 1 cm, the ratio is substantially less than one; in this case, the DCS optical density is predominantly sensitive to the extra-cerebral layer. At the 3 cm separation, the DCS optical density is more sensitive to cerebral blood flow than extra-cerebral blood flow at the short delay-times, i.e., the ratio is greater than one. However, at longer delay-times, the ratio decreases. (D) The ratio of the cerebral and extra-cerebral absorption components in the two-layer Modified Beer-Lambert law for DOS/NIRS, plotted as a function of ρ for a 10% increase in cerebral and extra-cerebral absorption. 〈L〉c and 〈L〉ec are the cerebral and extra-cerebral partial pathlengths [18, 21]. Notice from panels (C) and (D) that the DCS optical density is more sensitive to the cerebral layer than the NIRS optical density is, consistent with findings in work of reference [59].

(A) To monitor hemodynamics in the semi-infinite geometry, a juvenile pig’s scalp was reflected, and 2.5 mm burr holes were drilled through the skull for placement of 90-degree optical fibers. A DOS/NIRS source-detector pair (red circles) measured cerebral tissue absorption, and a DCS source-detector pair (black circles) measured cerebral blood flow. The source-detector separation of both pairs is ρ ≈ 1.5 cm. (B) Schematic showing the timeline of the experiment in minutes. Venous infusion of dinitrophenol (DNP, 9 mg/kg) dramatically stimulated cerebral oxygen metabolism and induced a 200% increase in cerebral blood flow. The DCS and DOS techniques were interleaved to measure blood flow and tissue absorption every 7 seconds. (C) Anterior-posterior slice of an anatomical MRI scan of a pig with similar weight to the juvenile pig used in this measurement. The burr holes for the two optical fibers closest to the midline in panel (A) have been artificially overlayed on this scan.

Fractional blood flow changes (i.e., F/F0 − 1) computed from applying the semi-infinite DCS Modified Beer-Lambert law (Eq. (4)) with assumed baseline optical properties of
μa0 (vertical axis) and
μs′0 (horizontal axis) to semi-infinite simulated data with noise (N = 1k curves). The actual blood flow and absorption changes are (A) 50% and 15%, and (B) −50% and −15%, respectively. Tissue scattering was constant, and the actual baseline properties (including simulated noise parameters) are identical to those in Fig. 5, e.g.,
μa0=0.1,
μs′0=8cm−1 (denoted by dashed lines). To compute the absorption changes from the simulated data, the Modified Beer-Lambert law (Eq. (1)) was employed. The differential pathlength (〈L〉) in Eq. (1) was calculated from the assumed baseline optical properties [84]. Finally, the baseline flow index, F0, was extracted from a nonlinear fit of the simulated baseline data to the semi-infinite correlation diffusion solution (Eq. (5)) evaluated at the assumed baseline optical properties. Errors in the assumed baseline optical properties only have small effects on the computed fractional flow change. Note that the computed fractional blood flow changes are not exactly 50% and −50% when the exact optical properties are assumed because of small errors arising from truncating the tissue absorption terms in the Taylor Series expansion of the DCS optical density (Eq. (3)) to first order.